This thesis studies the optimal trading problem with particular attention to frictions,
taking alpha signals as given in several practical settings in modern financial markets.
Chapter 2 provides a reduced-form model for price impact of market orders. As a scaling
limit of the econo-physics propagator model, it has both tractability for optimization
and good empirical fit. The nonlinearity in propagator model is explained as a effect of
intraday stochasticity of the market activity. Optimal trading strategies are given for the
case of stochastic alpha signal and volume signals in closed-form solutions. Moreoever,
concrete bounds for the absence of price manipulation strategies are provided.
Chapter 3 derives an actionable derivatives hedging strategy with both market and
limit orders from the perspective of a central risk book. It is found that limit order
is only beneficial for delta-hedging when the gamma of the risky position is negative.
Additionally, the interaction between transaction cost, adverse selection and risk aversion
can be characterized by a nonlinear PDE that describes the option price. According to
empirical analysis, tactical liquidity provision is beneficial for non-competitive market
makers for reasonable trading frequencies.
Chapter 4 studies the usage of display and nondisplay limit orders for order execution.
A price impact model is postulated and the corresponding scheduling algorithm is derived.
In the case where nondisplay limit order (hidden order) is used, there is a time which
separates the trading horizon into two regimes: the former only uses hidden order, and
the latter uses the mixture of limit and hidden orders. The effectiveness and robustness
of the algorithm is shown via numerical testing in both simulated data and NASDAQ
100 Index data.